MCQ
A possible value of $\tan \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right)$ is :
  • $\frac{1}{\sqrt{7}}$
  • B
    $2 \sqrt{2}-1$
  • C
    $\sqrt{7}-1$
  • D
    $\frac{1}{2 \sqrt{2}}$

Answer

Correct option: A.
$\frac{1}{\sqrt{7}}$
a
Let $\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}=\theta$

$\sin 4 \theta=\frac{\sqrt{63}}{8}$

$\cos 4 \theta=\frac{1}{8}$

$2 \cos ^{2} 2 \theta-1=\frac{1}{8}$

$\cos ^{2} 2 \theta=\frac{9}{16}$

$\cos 2 \theta=\frac{3}{4}$

$2 \cos ^{2} \theta-1=\frac{3}{4}$

$\cos ^{2} \theta=\frac{7}{8}$

$\cos \theta=\frac{\sqrt{7}}{2 \sqrt{2}}$

$\tan \theta=\frac{1}{\sqrt{7}}$

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